The Advanced X-ray Astrophysics Facility (AXAF) is scheduled for launch on September 1, 1998, on a mission lasting ten years. During this time AXAF will be subject to eclipses by the Earth and the Moon. Eclipses by the Earth will occur during regular 'seasons' six months apart. AXAF requires that none last longer than 120 minutes, and this constrains the orbit orientation. Eclipses by the Moon occur infrequently, but may pose serious operational problems. The AXAF perigee altitude can be chosen, once the other initial conditions are known, so that objectionable Moon-eclipses can be avoided by targeting the final burn.